A visit to the protected bays, remote lagoons and sleepy Mexican towns of Baja California is one of the world’s great road trips. Nature here is nearly as welcoming as in the Galápagos – curious grey whales come and greet you, sea turtles, sea lions and whale sharks swim by – but you can start and end your adventure in astonishing luxury. Why hadn’t I heard about it before?

The slender peninsula of lower, or Baja, California feels secret and secluded, like an island. On one side is the Pacific, on the other the Sea of Cortez, which separates it from the Mexican mainland on one side. It runs below the US California, which was lost by Mexico to the Americans in the 1800s. It’s a playground for Hollywood stars at the tip of the desert peninsula, at glamorous “Cabo”, and a haven for marine mammals in the secluded bays further north. Mosquitoes only turn up in August and September.

I flew to San José del Cabo (two and a half hours from LA and less from Mexico City) and recuperated in the rooftop Jacuzzi overlooking the ocean at the cool El Ganzo hotel. Artists who stay leave mementos; an octopus spreads its tentacles over one bedroom wall. Like everything about Baja, the octopus is unexpected and magical. In the warm evening air I wandered through the streets of quiet San José del Cabo, browsing the shops full of silver, watching the families spilling out into the main square.

The next day the expedition started early. My refined and knowledgeable naturalist guide drove me to La Paz, the capital of Baja Sud, where we breakfasted on large black coffees and cinnamon buns on the marina. I was fearful of a seven-hour trip on a 20ft low-bottomed boat without much cover out to the Espíritu Santo island in the Sea of Cortez. But it was worth the sunburn. Forget gloomy whale trips to spot distant flippers from large boats. This is full-on wonder: intimate encounters with wildlife that almost seemed to welcome us. Within half an hour of leaving the marina, we saw the largest fish in the world: a whale shark. This one, around eight metres long, floating idly by our boat, its grey-and-brown back pebbled with white spots and pale stripes. A few minutes later, a sea turtle paraded by us, head up. Next came a school of dolphins. As our boat turned round and round, they played in the amusement park of our wake.

Meanwhile in the distance, a humpback whale banged the water with its three-metre pectoral fins, spraying the unblemished blue sky. Soon we reached the island where a colony of sea lions lived. When we jumped off the side of the boat a young sea lion came to see me, his tawny face made strange and smooth by the water as he mirrored my movements, swirling under the boat.

the whale turned her head to look at me with one eye. my heart twisted as i felt her soft but firm skin

After a lunch of ceviche packed into crisp tacos on a deserted beach, we watched colonies of frigatebirds inflating their red pouches to attract females, and blue-footed boobies sitting on rocks blissfully unaware of the ridiculous nature of their bright-blue feet. You don’t have to travel to the Galápagos islands to see them after all.

Near the shore we plunged into the clear water to swim with a whale shark. Jacques Cousteau called the Sea of Cortez the “aquarium of the world”, because of the diversity and concentration of marine life. It would have been worth the journey here just for this one day.

Kayaking in crystal clear water off Espíritu Santo

Sea lions frolic beneath the surface

San Javier Mission near Loreto

Fish tacos with avocado salsa – a taste of the delicious cuisine on offer

Baja’s cactus-studded desert peninsula

The lounge at El Hotelito in Todos Santos

The rooftop pool at Hotel El Ganzo

Horse riding in Bahia Agua Verde

The next day we travelled on, up empty Highway One, flanked by cardon cacti sticking up like giant hands, from La Paz to the west side of the peninsula, the Pacific coast at Magdalena Bay. Our pretty white boat bounced over the waves, by sand dunes, accompanied by a fleet of pelicans, to the salty lagoon that is both discotheque and nursery for the world’s main grey whale population. The whales come from Alaska to mate, then return 11 months later to have their babies and let them grow up a little before taking them back on the 6,000-mile journey to Alaska. The whales approach the boats, rubbing against them, rising up to peer in. Sandbars separate the grey whales from the rip tides and huge waves of the Pacific.

The low-bottomed skiffs have to stay five metres from the calves and their mothers, though if the whales come up to the boats, that’s a different story. A grey whale about 16 feet long and three or four weeks old poked its head up by our white skiff. “Touch her. She wants the contact,” said the guide. The young whale turned her head to look at me with one eye and I stretched out my hand and my heart twisted as I felt the soft but firm skin and we looked at each other. The chasm between the species suddenly didn’t seem so huge. These whales have been interacting with humans like this for years, but my guide told me that each year they are more curious and less afraid, though in the days of more whaling they were referred to as “devil fish” because they fought so hard when caught.

After my encounter with the grey whale calf, I gorged on lobster and sea bass for a few dollars in La Unión, a rough-looking roadside fisherman’s café. The food was finer than in any London restaurant. As for me, I was unrecognisable: bright-eyed, all jaded city-tiredness and world-weariness gone. Every meal on the trip was excellent, from tacos and fajitas to bounteous seafood, all much less spicy than in mainland Mexico.

We travelled on. That night, walking along the boardwalk in sleepy Loreto, once the capital of all of California, I felt utterly happy; perhaps because of the contact with the whales, but also because along the empty desert roads of Baja there is a sense of escape and freedom and safety, away from the harsh modernised world. In Loreto, the only thing the 14-year-olds could do to be edgy was ride their new bikes a touch fast by the Sea of Cortez boardwalk. In the morning, a luxury boat, this time with plenty of shade, took us out to watch blue whales frolic in the penetratingly blue waters around the Coronado islands. By now I’d seen humpback, grey and blue whales, but this wasn’t about ticking off whale species, rather entering another way of thinking and feeling.

From Loreto, our car twisted and turned up the dirt road through the mountains by forests of 12ft-high cardon cacti, to one of the country’s first and best preserved Jesuit outposts. The San Javier Mission is in a little village with fruit trees and an olive tree, about 45 minutes from the town. Buy goat’s cheese and mango marmalade and feel the soul-calming stillness in this remote landscape. We were the only visitors.

After the blissful rough and tumble of the road trip through wild Baja – eating the best lobster ever in that roadside cafe, trying to learn Spanish as we drove hundreds of miles through the desert and mountain landscape without seeing a billboard, joining the locals in the town squares, watching the pelicans, the frigatebirds, the vultures – I didn’t want to return to the tourist world. But the last night on the road was at Todos Santos, a place of charm, history, art galleries and fine restaurants. I stayed at the excellent Guaycura Hotel in the middle of the town. It has a beach resort nearby, where my massage and mango facial was body-melting heaven. The masseuse gave me mango juice to drink as I watched the molten sun sink into the ocean. Perhaps civilisation has its moments.

But if you want faultless civilisation, your final stop has to be One&Only Palmilla in Los Cabos, where the food, the service, the spa, the rooms, are perfect, yet there is still that heady magic of Baja in the air. The hairdresser there managed to transform my hair as no one in London ever has, while at the pool, attendants even offered to polish my sunglasses. My room overlooked the beach and had its own plunge pool and butler. The rat pack used to hang out at Palmilla; now Hollywood stars like Jennifer Aniston party here. George Clooney held his 50th birthday bash at Palmilla. Why wouldn’t he? And with luck, you might see those humpback whales leaping in the Sea of Cortez beyond.